A few questions before I face what I think is the end boss...

[Mister Shan]

I just beat The Sundered Monarch and have a choice to go into the Rhogar Plane. I think this is the end? If I beat the game now does it automatically start the new game plus? I got screwed over by Dark Souls so I always check to make sure before I face the final boss on all souls games. If it does automatically take me into a new game plus, is there anything I should prep?

If it doesn't, after you beat it how do you start the new game plus and how should I prep? Might as well get that info now too.

[Swanky]

You're locked into the current ending. Beating the final encounter of this gives you the option to go back to the save outside the Rhogar realm and you can wrap up your business, start again in NG 0 or NG +1.
After beating the final encounter you will also have the option to start a new game file with extra options, such as the pre nerfed enemy placments, randomizers, etc. Not sure it will activate those on the current character's new game as I have not tried it myself.